A157029 A007318 * A157019.

1, 3, 7, 17, 39, 89, 203, 459, 1029, 2299, 5129, 11409, 25273, 55787, 122875, 270239, 593331, 1299883, 2841243, 6197855, 13499235, 29366411, 63809311, 138466835, 300036895, 649186659, 1402796793, 3027908077, 6529611587, 14068804905

Offset: 1

Author

Gary W. Adamson & Mats Granvik, Feb 21 2009

Keywords

• nonn

Comments

Equals row sums of triangle A157028.

Examples

			a(4) = 17 = (1, 3, 3, 1) dot (1, 2, 2, 4) = (1 + 6 + 6 + 4). a(4) = 17 = sum of row 4 terms, triangle A157028: (8 + 5 + 3 + 1).
G.f.: A(x) = x + 3*x^2 + 7*x^3 + 17*x^4 + 39*x^5 + 89*x^6 + 203*x^7 + 459*x^8 + 1029*x^9 + 2299*x^10 + ...
such that
A(x) = x/((1-x) - x) + x^2*(1-x)^2/((1-x)^2 - x^2)^2 + x^3*(1-x)^6/((1-x)^3 - x^3)^3 + x^4*(1-x)^12/((1-x)^4 - x^4)^4 + x^5*(1-x)^20/((1-x)^5 - x^5)^5 + ...
		

Crossrefs

Cf. A157019, A157028, A156348

Formula

G.f.: Sum_{n>=1} x^n * (1-x)^(n*(n-1)) / ((1-x)^n - x^n)^n. - Paul D. Hanna, Mar 26 2018

G.f.: Sum_{n>=1} x^n/(1-x)^n / (1 - x^n/(1-x)^n)^n. - Paul D. Hanna, Mar 26 2018

Extensions

Extended by R. J. Mathar, Apr 07 2009